Keukenhof and Hague daytrip

That's very well possible. It is less than 1 hr from Amsterdam Centraal to Den Haag Centraal, from where it is a 10-min walk to the Mauritshuis (not "Mauritius") museum.
For the Keukenhof it is best to take the train back to Leiden Centraal (15 mins), where you'll find the Keukenhof Express bus in front of the station, which takes you to the gardens.
After visiting, another Keukenhof Express bus takes you to Schiphol, where you can pick up the train to Amsterdam Centraal.

Added:
For your kids the train is almost free with the EUR 2,50 Railrunner ticket.
The square in front of the Mauritshuis (simply called "Plein") has excellent lunch facilities.

That may be the right order - after the Keukenhof you will all be very tired. Full of happiness and beauty but tired. And probably a little cramped - it gets crowded. I can happily spend 3 or 4 hours at Keukenhof and not see everything, and I know the layout well having visited numerous times.

You know your - and the munchkins' - stamina. I usually don't try to combine anything, except sometimes the parade or walks or rides through the neighbouring fields, with Keukenhof.

If you do enough planning, Den Haag, has a tram and bus system, so you could theoretically eliminate some of the urban walking. I don't see it as urgent for 8 and 5 to see the two (and more) excellent art museums there - although I love art museums myself. In particular the Gemeentmuseum is just immense.

Do you ever use public transportation at home? It's important to understand waiting around for public transit. And going to two places by transit in one day has a lot of waiting and sitting for people used to an SUV direct to the soccer field. Keukenhof is a special event, so transit to and from there is an addition. You can't make a continuous trip without retracing your steps. Like if you wanted to bus to a town north of Boston in the morning and a town south of Boston in the afternoon.

Note that Keukenhof is not just a few bulb beds. It's the equivalent of a medium-sized public garden anywhere else. And that's just settling for a view of the (separate) bulb fields visible downhill from the perimeter fence of Keukenhof. I'll guess that Keukenhof is as big as all of the formally planted areas at Tower Hill or Garden in the Woods (MA) but not including open meadows or forest walks in those places. There are also periodic entertainments, like a brass band or a barrel-organ concert, many dining options, and pop-up events around the Keukenhof property. Think Knott's Berry Farm but without the rides.

You know your family capabilities and interests, and because the season is so short, Keukenhof alone is a must for this trip. But Amsterdam is a very rich destination, including for young people. Taking a daytrip out of 3 days is a big loss of less exhausting visits within resting distance of your hotel in Amsterdam. Be careful about your planned pace for the whole trip.

going to two places by transit in one day has a lot of waiting and sitting
This is the Netherlands. All the trains needed run at least 4 times per hour, and the Keukenhof Express bus almost leaves continuously.

Wow, thanks for such great feedback!

We've used public transportation in NYC, Boston, and Portugal. I should add we are going on to Bruges and Paris after Amsterdam, with 2 days in Disneyland to reward them for being good travelers! I try to do museums early morning and something outdoors in the afternoon to let them get their energy out.

It is early days, but the public transport planner 9292.nl will give you real time information for all your transport needs.

Tom, don't be so sensitive. I am addressing AMERICAN auto drivers, not patriotic Nederlanders. There are many Americans who have never in their lives used public transportation. They think it's for poor people. (No idea about the OP personally.) I live in a suburb of New York City where many homes with two children have FIVE cars parked in their driveway every night. (The two-car garage is full of consumer goods ... )

I was born in NYC and took a half-hour subway ride to another borough for high school every day. In the early 60's, the NYC subway was superb.

I have spent plenty of time, on five trips to Amsterdam, waiting for the "right" tram to come to my stop. "Latency" is an important concept in scheduling and perceiving the frequency of any particular service. And don't forget the annoying one-time wait in line for a Chipkaart and likely problems with many USA Chip Credit Cards.

No hurt feelings, patriotic or otherwise, just a realistic picture of what to expect of the public transport.